16 problems

Let $\mathcal{Z}_k$ denote the $\mathbb{Q}$-space of multiple zeta values of weight $k$. Zagier's dimension conjecture. The generating series of their dimensions should satisfy … T…

Let $\mathsf{AMTV}_w$ be the $\mathbb{Q}$-vector space generated by all alternating multiple $T$-values of weight $w$, and write $d_w=\dim_{\mathbb{Q}}\mathsf{AMTV}_w$ for…

Let $q$ be a prime power. For $w\in\mathbb N$, define … and, for $w>q$, set … Let $\mathcal Z_w$ be the $K$-span of the positive-characteristic multiple zeta values of weight $w$,…

Let $\mathcal{E}_k$ be the weight-$k$ component of the algebra of multiple Eisenstein series. Define the generating series for modular forms and cusp forms by … Here…

For each weight $n$, let $\mathsf{AMSV}_n$ denote the rational vector space of alternating multiple $s$-values. Recurrence dimension conjecture. … and, for every $n\ge3$, … The pap…

For each $n\ge2$, let $\mathsf{AMtV}_n$ denote the rational vector space of alternating multiple $t$-values of weight $n$. Exponential dimension conjecture. … The paper lists this…

For each weight $n$, let $\mathsf{AMTV}_n$ denote the rational vector space of alternating multiple two-one values of weight $n$. Tribonacci dimension conjecture. The generating fu…

Top-component dimension conjecture. If $\dim(V_d)=d$, then

Let $\FES_{w,1}$ denote the $\Q$-vector space of finite Euler sums of weight $w$ and superbity one, and set $f_w=\dim_{\Q}\FES_{w,1}$ for $w\ge1$. Finite Euler-sum dimension conjec…

For each positive integer $w$, let $\FMZ_{w,2}$ be the $\Q$-vector space generated by finite multiple zeta values of weight $w$ and superbity two. Define $d_{0,2}=1$ and…

For positive integers $w$ and $\ell$, let $\FMZ_{w,\ell}$ be the $\Q$-vector space generated by finite multiple zeta values of weight $w$ and superbity $\ell$. Arbitrary-superbity…

For weight $k$, let $eds_k$ denote the dimension of the span of the extended double-shuffle relations $ds(u,v)$ with $|u|+|v|=k$, $u\in\mathfrak H^0$, and…

Let $\operatorname{q\mathcal{M}\mathcal{Z}}$ be the space of multiple Eisenstein series and $\operatorname{q\mathcal{M}\mathcal{Z}}^\shuffle$ the space spanned by shuffle multiple…

Let ${\mathbf Z}_w^{\rm O}$ be the $\Q$-vector space generated by Okounkov's type O $q$-multiple zeta values $\frakz_q^{\rm O}[\bfs]$ with $|\bfs|\leq w$. Okounkov's dimension conj…

Let $d'(k,l)$ denote the dimension values associated with the bigraded spaces $\operatorname{gr}^{\operatorname{W},\operatorname{L}}_{k,l}(\operatorname{q\mathcal{M}\mathcal{Z}})$,…

Prime-level weight-three conjecture.